Optimal control of intermittent normal conduction in a tachycardia-dependent right bundle branch block.

Abstract

Tachycardia-dependent right bundle branch block (RBBB) with atrial fibrillation in a patient under digitalis therapy is presented, in which supernormal phase of intraventricular conduction was well-documented. The development of long intervals terminated by a normally conducted beat was attributed to the occurrence of concealed atrio-ventricular (A-V) conduction of the atrial fibrillation impulse during the supernormal phase. The ventricular interval caused by a normally conducted beat (xs) in the interval of 1.01-1.63 s was transformable into a vector differential equation dy/dx = In (x + a) + 1, where parameter a = 0, 0.04, 0.08, 0.16, and 0.24. This is piecewise continuous and integrable. The function in (x + 0.04) + 1 was considered to give the solution of the problem of optimal control, which is equivalent to the problem of finding Green's function of the region, i.e. to solving the Dirichlet problem. The solution curves, given by y = (x + a) in (x + a) + 1, can be interpreted as distributions. There were structurally stable vector field points on a differentiable manifold, i.e, attractors. In general, the modelling may be applicable to tachycardia-dependent RBBB.